= A5 root system
{c}
{title2=$A_5$}
The <root system> of the complex <special linear Lie algebra> $\mathfrak{sl}_6(\mathbb C)$ is $\{e_i-e_j:1\le i\ne j\le6\}$ in $\sum_ix_i=0$. Its <simple roots> $e_i-e_{i+1}$ give a five-node <An Dynkin diagram>. The defining <fundamental representation> has six <weights> $w_i=e_i-\tfrac16\sum_je_j$. The <dual representation> has <weights> $-w_i$, and the <two-index antisymmetric representation> has fifteen <weights> $w_i+w_j$, $i<j$, all with <weight multiplicity> one.
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